The mass-to-flux ratio in molecular clouds. What are we really measuring?

Abstract: The mass-to-magnetic flux ratio of molecular clouds is a parameter of central importance as it quantifies the dynamical significance of the magnetic field with respect to gravitational forces. Therefore, it can provide invaluable information on the fate of clouds, and the sites of star formation. Our objective was to study the accuracy with which we can measure the true mass-to-flux ratio in molecular clouds under various projection angles and identify systematic biases. We used a 3D nonideal magnetohydrodynamic chemo-dynamical simulation of a turbulent collapsing molecular cloud. We quantified the accuracy with which the mass-to-flux ratio is recovered under various projection angles and dynamical stages by analyzing the magnetic field - gas column density relation, and comparing the "observed" mass-to-flux ratio against the true values. We find that projection effects have a major effect on measurements of the mass-to-flux ratio. Zeeman measurements can overestimate the true mass-to-flux ratio of the cloud by more than an order of magnitude when the magnetic field primarily lies on the plane of the sky. Therefore, measurements of the mass-to-flux ratio based on Zeeman observations should be considered as upper limits. Mass-to-flux ratio estimates inferred from polarization observations do not provide a physically meaningful probe of the true mass-to-flux ratio and can lead to unphysical results as they fail to capture the underlying correlation between the magnetic field and column density.